Question : Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received 1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received 20 more as annual interest. How much money did he invest in each scheme ?
CBSE 2025
Solution :
Let amount invested by Vijay at 8% interest rate be ₹ x
and the amount invested by Vijay at 9% interest rate be ₹ y
We know,
Simple Interest (SI) = [Principle×Rate×Time]/100
Here Time is 1 Year in both the case.
SI on Amount of ₹ x which is invested at 8% interest rate
= [Principle×Rate×Time]/100
= [x×8×1]/100
= 8x/100
SI on Amount of ₹ y which is invested at 9% interest rate
= [Principle×Rate×Time]/100
= [y×9×1]/100
= 9y/100
ATQ
8x/100 + 9y/100 = 1860
(8x+9y)/100 = 1860
8x+9y=186000 — (1)
Similarly
9x+8y= (1860+20)×100
9x+8y=188000 — (2)
Solving equation (1) and (2)
[8x+9y=186000] ×9
[9x+8y=188000] ×8
72x+81y=1674000
72x+64y=1504000
- - -
----------------------------
0 + 17y = 170000
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17y=170000
y=170000/17
y=10000
putting in equation (1)
8x+9[10000]=186000
8x+90000=186000
8x=186000-90000
8x=96000
x=96000/8
x=12000
Hence, money invested in scheme A is ₹12000 and scheme B is ₹10000.